Bezier path moving during animation when it should not
There are several ways to do it:


F3 and type Remove Animation.
You can delete the animation in the Outliner: Select the object, unfold its tree, right click on Animation and choose Clear Animation Data.
Open the Dopesheet, switch it to Action Editor mode, you have a dropdown menu with all your animations, close the selected animation with X.


As your curve was the only user of this animation, it won't be reloaded when you'll reopen the file. If you don't want to loose it, in the Dopesheet / Action Editor mode, on the right of the action name (it has now a 0 which means no user), press on the shield icon.